EM2INV - a finite difference based algorithm for two-dimensional inversion of geoelectromagnetic data

Abstract

The paper presents an efficient finite difference based 2D-inversion algorithm, EM2INV, for geoelectromagnetic data. The special features of the algorithm are • optimal grid generation based on grid design thumb rules, • finite domain boundary conditions, • interpolation matrix that permits generation of response at observation points different from grid points, • Gaussian elimination forward matrix solver, that enables reuse of already decomposed coefficient matrix, • super-block notion that reduces the number of blocks with unknown resistivities and, in turn, the size of Jacobian matrix and • bi-conjugate gradient matrix solver for inverse problem which circumvents the need of explicit Jacobian matrix computation. The algorithm is tested rigorously by setting up exercises of diverse nature and of practical significance. The stability of the algorithm is established by inverting the synthetic response corrupted with Gaussian noise. The inversion experiments are aimed at studying • relative performance of response functions, • inversion quality of E- and B-polarization data, • efficacy of single and multi-frequency data inversion, • minimum number of frequencies and observation points needed for successful data inversion. It has been observed that the Magneto-telluric data deciphers better the vertical position of the target and Geomagnetic Depth Sounding data deciphers the horizontal variations in a better way. The conductive and resistive bodies are better resolved by inversion of E- and B-polarization data respectively. The results of multi-frequency inversion imply that the increase in the number of frequencies does not necessarily enhance the inversion quality especially when the spread of observation points is sufficiently large to sense the target. The study of a minimum number of observation points highlights the importance of single point inversion that furnishes useful information about the inhomogeneity.